\psset{unit=1,algebraic}
\begin{pspicture*}(-1,-0.5)(3.5,2.5)
\psaxes[ticks=none,labels=none]{<->}(0,0)(-0.5,-0.5)(3.5,2.5)
\psplot[linecolor=blue]{0.5}{3.1}{2-(x-1.8)^2}
\psline[linecolor=red,linestyle=dashed](1.8,0)(1.8,2)(0,2)
\psline[linecolor=red,linestyle=dashed](1,0)(1,1.36)(0,1.36)
\footnotesize
\psxTick[ticksize=-3pt 0,labelsep=3pt](1.8){x_0}
\psxTick[ticksize=-3pt 0,labelsep=3pt](1){x}
\psyTick[ticksize=-3pt 0,labelsep=3pt](2){f(x_0)}
\psyTick[ticksize=-3pt 0,labelsep=3pt](1.36){f(x)}
\psyTick[ticksize=0,labelsep=10pt](1.72){\rotateleft{\leq}}
\rput(0.5,0){$($}
\psxTick[ticksize=-3pt 0,labelsep=3pt](0.5){x_0-\delta}
\rput(3.1,0){$)$}
\psxTick[ticksize=-3pt 0,labelsep=3pt](3.1){x_0+\delta}
\psdot[linecolor=green](1.8,2)
\end{pspicture*}